Finite Element and Reduced Dimension Methods for Partial Differential Equations
Description
This book aims to provide with some approaches for lessening the unknowns of the FE methods of unsteady PDEs. It provides a very detailed theoretical foundation of finite element (FE) and mixed finite element (MFE) methods in the first 2 chapters, and then Chapter 3 provides the FE and MFE methods to solve unsteady partial differential equations (PDEs). In the following 2 chapters, the principle and application of two proper orthogonal decomposition (POD) methods are introduced in detail.
This book can be used as both the introduction of FE method and the gateway to the FE frontier. For readers who want to learn the FE and MFE methods for solving various steady and unsteady PDEs, they will find the first 3 chapters very helpful. While those who care about engineering applications may jump to the last 2 chapters that introduce the construction of dimension reduction models and their applications to practical process calculations. This part could help them to improve the calculation efficiency and save CPU runtime so as to do wonders for their engineering calculations.
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Zhendong Luo has been engaged in the research on numerical solutions of partial differential equations (PDEs) in computational mathematics since 1986. His main research interests are finite element method and computational fluid dynamics and its numerical simulation. He has hosted and participated in more than 20 scientific research projects supported by National Natural Science Foundation of China or provincial and ministerial department. Luo has published a monograph and more than 260 research papers.
Content
Preface.- Basic Theory of Standard Finite Element Method.- Basic Theory of Mixed Finite Element Method.- Mixed Finite Element Methods for the Unsteady Partial Differential Equations.- The Reduced Dimension Methods of Finite Element Subspaces for Unsteady Partial Differential Equations.- The Reduced Dimension of Finite Element Solution Coefficient Vectors for Unsteady Partial Differential Equations.- Bibliography.- Index.